A related class of distributed controllers are those based on Graph Neural Networks (GNNs). GNNs can be viewed as graph filters followed by pointwise nonlinear activation functions [1]}, and among other favorable properties, enjoy stability to graph perturbations [2]}. While recent use of GNNs for distributed control has shown promise [3]}, [4]}, [5]}, such results currently lack strong guarantees of stability. We believe the results in this paper are a first step towards addressing this gap in the literature, by explicitly connecting graph filters and distributed optimal controllers. The direct relationship between graph filters and GNNs suggests that understanding the former will give insight in the effects of the latter.
